Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions.

It is well known that the central problem of the whole of modern mathematics is the study of transcendental functions defined by differential equations.

Every one who understands the subject will agree that even the basis on which the scientific explanation of nature rests is intelligible only to those who have learned at least the elements of the differential and integral calculus, as well as analytical geometry.

Projective geometry has opened up for us with the greatest facility new territories in our science, and has rightly been called the royal road to our particular field of knowledge.

The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal calculus, although the eighteenth century shyness toward it had long lost all point.

Mathematics in general is fundamentally the science of self-evident things.

Among mathematicians in general, three main categories may be distinguished; and perhaps the names logicians, formalists, and intuitionists may serve to characterize them.